Is there a formula to calculate ground distance traveled given rate of climb and true airspeed? - Aviation Stack Exchange most recent 30 from aviation.stackexchange.com 2019-11-12T16:23:04Z https://aviation.stackexchange.com/feeds/question/37721 https://creativecommons.org/licenses/by-sa/4.0/rdf https://aviation.stackexchange.com/q/37721 1 Is there a formula to calculate ground distance traveled given rate of climb and true airspeed? Yohji https://aviation.stackexchange.com/users/21579 2017-05-04T13:56:52Z 2017-05-04T15:39:07Z <p>I'm looking for a formula to calculate the horizontal distance (guess it is the <em>Ground Distance</em>) passed during the phase of ascent (or descent), having the <em>rate of climb</em> in ft/min and the <em>TAS</em> in knots. I did not found a clear answer about this question. I think it may concern with the <em>Climb Gradient</em>.</p> <p>Refering to the image below, I'm trying to calculate <em>d</em>, having:</p> <ul> <li>h = 11200 ft</li> <li>RoC = 1250 ft/min</li> <li>TAS = 75 kn</li> </ul> <p><a href="https://i.stack.imgur.com/U7nx3.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/U7nx3.jpg" alt="Rectangle"></a></p> <blockquote> <p><em>ClimbGradient</em> = (<em>RoC</em> / <em>TAS</em>) * 6000 / 6076,12 = (1250 / 75) * 0.9874 = 16.45%</p> <p><em>d</em> = <em>h</em> / (<em>ClimbGradient</em> * 100) = 11200 / 1645.78711 = 6.80525 nm</p> </blockquote> <p>Is this correct calculation? I will update this question with the correct formula in other case.</p> https://aviation.stackexchange.com/questions/37721/-/37724#37724 0 Answer by Koyovis for Is there a formula to calculate ground distance traveled given rate of climb and true airspeed? Koyovis https://aviation.stackexchange.com/users/21091 2017-05-04T14:41:48Z 2017-05-04T14:41:48Z <p>Pythagoras has your answer.</p> <p>You've been climbing for 11200/1250 = 8.96 minutes</p> <p>In that time you've traveled 75 * 8.96/60 = 11.2 nautical miles = 68,051 ft along the diagonal D</p> <p>$D^2$ = $d^2$ + $h^2$ => d = 67,123 ft = 11.05 nm</p> https://aviation.stackexchange.com/questions/37721/-/37725#37725 2 Answer by ymb1 for Is there a formula to calculate ground distance traveled given rate of climb and true airspeed? ymb1 https://aviation.stackexchange.com/users/14897 2017-05-04T14:42:03Z 2017-05-04T15:39:07Z <p>You need ground speed not TAS. GS is affected by the head- or tail-wind components.</p> <p>Assuming in your example GS is 75 knots, then just check how long it takes to change altitude.</p> <p>11,200 ft at 1,250 ft/min takes 8.96 minutes, or 0.1493 hours.</p> <p>At a speed of 75 knots, that's 11.2 NM.</p> <p>$$\frac{\text{altitude change (ft)}}{\text{rate of climb (ft/min)}\cdot60}\cdot\text{ground speed (knots)}$$</p> <hr> <p>Since the density of air changes during a climb/descent, it affects the rate of climb/descent. Fancy planes have <em>green bananas</em> or similar indications on the navigation display to show where you'll reach the target altitude (it updates in real-time).</p> <p><a href="https://i.stack.imgur.com/e0777.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/e0777.png" alt="enter image description here"></a><BR>The green arc is that green banana (altitude range arc).</p>